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A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity.
Equations of continuity state that if there are no sources or sinks, then the total mass within a volume element must stay the same.
Equations of continuity can be applied to other scenarios too, such as for conservation of electric charge rather than mass.
For Fluid Flow, the equations of continuity are:
If the fluid is incompressible: